Method for determining microstructure of titanium alloy and method for producing titanium alloy

ABSTRACT

A method for determining a microstructure of a titanium alloy includes determining a microstructure morphology of a titanium alloy based on a relational expression including a mechanical property parameter relating to a mechanical property of the titanium alloy, a microstructure parameter relating to a microstructure of the titanium alloy, and a composition parameter relating to a composition of the titanium alloy.

TECHNICAL FIELD

The present disclosure relates to a method for determining a microstructure of a titanium alloy and a method for producing a titanium alloy.

BACKGROUND ART

Titanium alloys having light weight, high strength, and excellent corrosion resistance are widely used in various fields such as power generation plants, chemical plants, aircrafts, and automobiles.

The mechanical properties of titanium alloys vary with the type and the amount of additive element and conditions of heat treatment, etc. Therefore, the type and the amount of additive element and conditions of heat treatment are changed to obtain mechanical properties in accordance with use of titanium alloys (see Patent Document 1).

CITATION LIST Patent Literature

Patent Document 1: JP366631513

SUMMARY

For instance, in an α+β titanium alloy such as Ti-6Al-4V alloy, the volume fraction of the α phase in the microstructure and the width of the acicular structure can be controlled by heat treatment. As the microstructure morphology such as the volume fraction of the α phase in the microstructure and the width of the acicular structure changes, the mechanical properties of the alloy changes.

The mechanical properties include various strength properties such as strength (room-temperature strength, high-temperature strength (creep strength)), impact property, toughness, and fatigue property. Although each property can be improved by controlling the microstructure, there are some combinations of properties which are incompatible or conflicting with each other in improving multiple strength properties. For instance, in an α+β titanium alloy, the α phase structure of equiaxed grains contributes to the improvement of e.g., fatigue limit value, but does not much contribute to the improvement of e.g., fracture toughness. Further, for instance, in an α+β titanium alloy, the acicular structure contributes to the improvement of e.g., fracture toughness, but does not much contribute to the improvement of e.g., fatigue limit value. Therefore, for instance, some α+β titanium alloys have a bi-modal structure combinedly having the α phase structure of equiaxed grains and the acicular structure to balance, for instance, toughness and fatigue property.

The mechanical properties of titanium alloys also vary with the type and the amount of additive element, as described above. Accordingly, it is necessary for titanium alloys to consider a parameter relating to the microstructure morphology and a parameter relating to the composition of the titanium alloys to balance mechanical properties, such as toughness and fatigue property, which tend to conflict in relation to the microstructure morphology, for instance. Therefore, it is not easy to determine the aforementioned various parameters to obtain a desired mechanical property in titanium alloys.

In view of the above, an object of at least one embodiment of the present invention is to provide a method for determining a microstructure of a titanium alloy to obtain a titanium alloy well balanced with respect to incompatible or conflicting mechanical properties.

(1) A method for determining a microstructure of a titanium alloy according to at least one embodiment of the present invention comprises determining a microstructure morphology of a titanium alloy based on a relational expression including a mechanical property parameter relating to a mechanical property of the titanium alloy, a microstructure parameter relating to a microstructure of the titanium alloy, and a composition parameter relating to a composition of the titanium alloy.

With the above method (1), by substituting a desired mechanical property for the mechanical property parameter in the relational expression and substituting the composition of the titanium alloy for the composition parameter in the relational expression, it is possible to obtain a condition which the microstructure parameter has to meet in order to achieve the desired mechanical property. Accordingly, for instance, by performing heat treatment of the titanium alloy so as to obtain microstructure morphology that meets the above condition, it is possible to obtain a titanium alloy having the desired mechanical property. Thus, it is possible to easily determine the microstructure morphology of the titanium alloy to obtain a titanium alloy well balanced with respect to incompatible or conflicting mechanical properties.

(2) In some embodiments, in the above method (1), the mechanical property parameter includes a parameter relating to a fatigue property, and a parameter relating to at least one of toughness or creep strength, the microstructure parameter includes a parameter relating to equiaxed α phase area ratio, and a parameter relating to lamellar layer spacing, and the composition parameter includes at least a parameter relating to aluminum content.

For instance, in an α+β titanium alloy, the α phase structure of equiaxed grains contributes to the improvement of e.g., fatigue property, but does not much contribute to the improvement of e.g., toughness and creep strength. Further, for instance, in an α+β titanium alloy, the acicular structure contributes to the improvement of e.g., toughness and creep strength, but does not much contribute to the improvement of e.g., fatigue property. That is, fatigue property tends to conflict with toughness and creep strength in relation to the microstructure morphology.

Further, for instance, in an α+β titanium alloy, the influence of aluminum on toughness of the alloy is larger than the influence of other additive elements.

In view of this, in the above method (2), by substituting respective values of the parameter relating to fatigue property, the parameter of at least one of toughness or creep strength, and the parameter relating to aluminum content into the relational expression in (1), it is possible to obtain a condition which the parameter relating to equiaxed α phase area ratio and the parameter relating to lamellar layer spacing have to meet. Further, when a value of one of the parameter relating to equiaxed α phase area ratio or the parameter relating to lamellar layer spacing is determined, a value of the other is also determined.

Accordingly, with the above method (2), by performing heat treatment of the titanium alloy so as to obtain microstructure morphology for achieving the values of the parameter relating to equiaxed α phase area ratio and the parameter relating to lamellar layer spacing as determined above, it is possible to achieve a desired state of mechanical properties which tend to conflict in relation to the microstructure morphology.

(3) In some embodiments, in the above method (2), the composition parameter further includes at least one of a parameter relating to nitrogen content, a parameter relating to iron content, or a parameter relating to hydrogen content.

With the above method (3), it is possible to determine the microstructure morphology of the titanium alloy in consideration of the influence of content of at least one of nitrogen, iron, or hydrogen.

(4) In some embodiments, in the above method (3), when the parameter relating to creep strength is YS [MPa], the parameter relating to toughness is KIC [MPa√m], the parameter relating to the fatigue property is σw [MPa], the parameter relating to equiaxed a phase area ratio is Vα [%], the parameter relating to lamellar layer spacing is DL [μm]. the parameter relating to aluminum content is Al [mass %], the parameter relating to nitrogen content is N [mass %], the parameter relating to iron content is Fe [mass %], the parameter relating to hydrogen content is H [mass %], a first constant is Const1, and a1, a2, b1, b2, b3, c1, c2, c3, and c4 each represent a coefficient, the relational expression is represented by the following expression (1):

a1×DL−a2×Vα=b1×YS+b2×σw+b3×KIC+c1×Al−c2×N−c3×Fe+c4×H−Const1   (1),

wherein the coefficient a1 is 30 or more and 300 or less, the coefficient a2 is 1 or more and 10 or less, the coefficient b1 is 0.5 or more and 5 or less, the coefficient b2 is 0.1 or more and 2 or less, the coefficient b3 is 5 or more and 50 or less, the coefficient c1 is 100 or more and 150 or less, the coefficient c2 is 1000 or more and 20000 or less, the coefficient c3 is 400 or more and 5000 or less, the coefficient c4 is 500 or more and 5000 or less, and the first constant Const1 is 1000 or more and 20000 or less.

With the above method (4), on the basis of the expression (1), it is possible to easily determine the microstructure morphology of the titanium alloy to obtain a titanium alloy well balanced with respect to incompatible or conflicting mechanical properties.

(5) In some embodiments, in the above method (3), the composition parameter further includes at least one of a parameter relating to carbon content or a parameter relating to vanadium content.

With the above method (5), it is possible to determine the microstructure morphology of the titanium alloy in consideration of the influence of content of at least one of carbon or vanadium.

(6) In some embodiments, in the above method (5), when the parameter relating to creep strength is YS [MPa], the parameter relating to toughness is KIC [MPa√m], the parameter relating to the fatigue property is σw [MPa], the parameter relating to equiaxed α phase area ratio is Vα [%], the parameter relating to lamellar layer spacing is DL [μm], the parameter relating to aluminum content is Al [mass %], the parameter relating to nitrogen content is N [mass %], the parameter relating to iron content is Fe [mass %], the parameter relating to hydrogen content is H [mass %], the parameter relating to carbon content is C [mass %], the parameter relating to vanadium content is V [mass %], a second constant is Const2, and a1, a2, b1, b2, b3, c1, c2, c3, c4, c5, and c6 each represent a coefficient, the relational expression is represented by the following expression (2):

a1×DL−a2 Vαb1×YS+b2×σw+b3×KIC+c1×Al−c2×N−c3×Fe+c4×H−c5×C+c6×V−Const2 (2),

wherein the coefficient a1 is 30 or more and 300 or less, the coefficient a2 is 1 or more and 10 or less, the coefficient b1 is 0.5 or more and 5 or less, the coefficient b2 is 0.1 or more and 2 or less, the coefficient b3 is 5 or more and 50 or less, the coefficient c1 is 100 or more and 150 or less, the coefficient c2 is 1000 or more and 20000 or less, the coefficient c3 is 400 or more and 5000 or less, the coefficient c4 is 500 or more and 5000 or less, the coefficient c5 is 500 or more and 5000 or less, the coefficient c6 is 10 or more and 200 or less, and the second constant Const2 is 1000 or more and 20000 or less.

With the above method (6), on the basis of the expression (2), it is possible to easily determine the microstructure morphology of the titanium alloy to obtain a titanium alloy well balanced with respect to incompatible or conflicting mechanical properties.

(7) A method for producing a titanium alloy according to at least one embodiment of the present invention comprises: a step of calculating a condition which the microstructure parameter has to meet, based on the relational expression in the above method (1), a step of determining a value of the microstructure parameter, based on the condition, a step of setting a heat treatment condition for achieving the determined value of the microstructure parameter, and a step of performing heat treatment under the set heat treatment condition.

With the above method (7), by substituting a desired mechanical property for the mechanical property parameter in the relational expression and substituting the composition of the titanium alloy for the composition parameter in the relational expression, it is possible to obtain a condition which the microstructure parameter has to meet in order to achieve the desired mechanical property, and it is possible to determine a value of the microstructure parameter based on the condition.

Further, with the above method (7), it is possible to set the heat treatment condition of the titanium alloy so as to obtain microstructure morphology corresponding to the determined microstructure parameter.

Further, with the above method (7), by performing heat treatment on the titanium alloy under the set heat treatment condition, it is possible to obtain a titanium alloy having the desired mechanical property. Thus, it is possible to obtain a titanium alloy well balanced with respect to incompatible or conflicting mechanical properties.

(8) In some embodiments, in the above method (7), the microstructure parameter includes a parameter relating to equiaxed α phase area ratio, and a parameter relating to lamellar layer spacing, and the step of determining the value of the microstructure parameter includes: a first determination step of determining a value of one parameter of the parameter relating to equiaxed α phase area ratio or the parameter relating to lamellar layer spacing, and a second determination step of determining a value of the other parameter of the parameter relating to equiaxed α phase area ratio or the parameter relating to lamellar layer spacing, based on the value of the one parameter determined in the first determination step and the condition.

With the above method (8), it is possible to obtain a condition which the parameter relating to equiaxed α phase area ratio and the parameter relating to lamellar layer spacing have to meet, based on the relational expression.

Further, with the above method (8), when a value of one of the parameter relating to equiaxed α phase area ratio or the parameter relating to lamellar layer spacing is determined, a value of the other is also determined based on the condition.

(9) In some embodiments, in the above method (8), the first determination step includes determining the parameter relating to equiaxed α phase area ratio, and the second determination step includes determining the parameter relating to lamellar layer spacing.

For instance, in an α+β titanium alloy, the area ratio of the α phase structure of equiaxed grains (equiaxed α phase area ratio) in the microstructure is mainly affected by solution temperature at heat treatment. Further, for instance, in an α+β titanium alloy, the width of the acicular structure (lamellar layer spacing) in the microstructure is mainly affected by cooling rate at solution treatment in heat treatment.

Accordingly, with the above method (9), since the parameter relating to equiaxed a phase area ratio can be determined in the first determination step prior to the second determination step, it is possible to preferentially determine a condition of solution temperature.

(10) In some embodiments, in the above method (8), the first determination step includes determining the parameter relating to lamellar layer spacing, and the second determination step includes determining the parameter relating to equiaxed α phase area ratio.

As described above, for instance, in an α+β titanium alloy, the area ratio of the a phase structure of equiaxed grains (equiaxed α phase area ratio) in the microstructure is mainly affected by solution temperature at heat treatment, and the width of the acicular structure (lamellar layer spacing) in the microstructure is mainly affected by cooling rate at solution treatment in heat treatment.

Accordingly, with the above method (10), since the parameter relating to lamellar layer spacing can be determined in the first determination step prior to the second determination step, it is possible to preferentially determine a condition of cooling rate at heat treatment.

(11) In some embodiments, in the above method (7), the method further comprises: a step of preparing a specimen by performing heat treatment under the set heat treatment condition; a step of evaluating a mechanical property of the specimen; a step of determining whether the microstructure parameter determined in the step of determining the value of the microstructure parameter is appropriate, based on an evaluation result in the step of evaluating the mechanical property of the specimen; and a step of modifying at least one of the value of the microstructure parameter or a value of the composition parameter if it is determined that the value of the microstructure parameter is not appropriate in the step of determining whether the microstructure parameter is appropriate.

With the above method (11), by evaluating the mechanical property of the specimen and modifying at least one of the value of the microstructure parameter or the value of the composition parameter based on the evaluation result, it is possible to obtain a titanium alloy having the desired mechanical property.

(12) In some embodiments, in the above method (8), the method further comprises: a step of preparing a specimen by performing heat treatment under the set heat treatment condition; a step of evaluating a mechanical property of the specimen; a step of determining whether the microstructure parameter determined in the step of determining the value of the microstructure parameter is appropriate, based on an evaluation result in the step of evaluating the mechanical property of the specimen; and a step of modifying at least one of the value of the microstructure parameter or a value of the composition parameter if it is determined that the value of the microstructure parameter is not appropriate in the step of determining whether the microstructure parameter is appropriate.

With the above method (12), by evaluating the mechanical property of the specimen and modifying at least one of the value of the microstructure parameter or the value of the composition parameter based on the evaluation result, it is possible to obtain a titanium alloy having the desired mechanical property.

(13) In some embodiments, in the above method (9), the method further comprises: a step of preparing a specimen by performing heat treatment under the set heat treatment condition: a step of evaluating a mechanical property of the specimen; a step of determining whether the microstructure parameter determined in the step of determining the value of the microstructure parameter is appropriate, based on an evaluation result in the step of evaluating the mechanical property of the specimen; and a step of modifying at least one of the value of the microstructure parameter or a value of the composition parameter if it is determined that the value of the microstructure parameter is not appropriate in the step of determining whether the microstructure parameter is appropriate.

With the above method (13), by evaluating the mechanical property of the specimen and modifying at least one of the value of the microstructure parameter or the value of the composition parameter based on the evaluation result, it is possible to obtain a titanium alloy having the desired mechanical property.

(14) In some embodiments, in the above method (10), the method further comprises: a step of preparing a specimen by performing heat treatment under the set heat treatment condition; a step of evaluating a mechanical property of the specimen; a step of determining whether the microstructure parameter determined in the step of determining the value of the microstructure parameter is appropriate, based on an evaluation result in the step of evaluating the mechanical property of the specimen; and a step of modifying at least one of the value of the microstructure parameter or a value of the composition parameter if it is determined that the value of the microstructure parameter is not appropriate in the step of determining whether the microstructure parameter is appropriate.

With the above method (14), by evaluating the mechanical property of the specimen and modifying at least one of the value of the microstructure parameter or the value of the composition parameter based on the evaluation result, it is possible to obtain a titanium alloy having the desired mechanical property.

According to at least one embodiment of the present invention, it is possible to easily determine the microstructure morphology of a titanium alloy to obtain a titanium alloy well balanced with respect to incompatible or conflicting, mechanical properties.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a table showing the influence of microstructure morphology on mechanical properties of α+β titanium alloys.

FIG. 2 is a view showing microstructure examples of the equiaxed α phase, the acicular structure, and the bimodal structure including the equiaxed α phase and the acicular structure.

FIG. 3 is a flowchart for describing a process of a method for producing a titanium alloy according to some embodiments.

FIG. 4 is a flowchart for describing a process of determining a value of a microstructure parameter in a microstructure parameter determination step S20 according to some embodiments.

FIG. 5 is a diagram showing an example of temperature change in heat treatment of a titanium alloy.

FIG. 6 is a flowchart for describing a process of treatment in a property evaluation step S40 according to some embodiments.

DETAILED DESCRIPTION

Embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It is intended, however, that unless particularly identified, dimensions, materials, shapes, relative positions and the like of components described in the embodiments shall be interpreted as illustrative only and not intended to limit the scope of the present invention.

For instance, an expression of relative or absolute arrangement such as “in a direction”, “along a direction”, “parallel”, “orthogonal”, “centered”, “concentric” and “coaxial” shall not be construed as indicating only the arrangement in a strict literal sense, but also includes a state where the arrangement is relatively displaced by a tolerance, or by an angle or a distance whereby it is possible to achieve the same function.

For instance, an expression of an equal state such as “same” “equal” and “uniform” shall not be construed as indicating only the state in which the feature is strictly equal, but also includes a state in which there is a tolerance or a difference that can still achieve the same function.

Further, for instance, an expression of a shape such as a rectangular shape or a cylindrical shape shall not be construed as only the geometrically strict shape, but also includes a shape with unevenness or chamfered corners within the range in which the same effect can be achieved.

On the other hand, an expression such as “comprise” “include”, “have”, “contain” and “constitute” are not intended to be exclusive of other components.

Titanium alloys having light weight, high strength, and excellent corrosion resistance are widely used in various fields such as power generation plants, chemical plants, aircrafts, and automobiles.

The mechanical properties of titanium alloys vary with the type and the amount of additive element and conditions of heat treatment, etc. Therefore, the type and the amount of additive element and conditions of heat treatment are changed to obtain mechanical properties in accordance with use of titanium alloys.

For instance, in an α+β titanium alloy such as Ti-6Al-4V alloy, the volume fraction of the α phase in the microstructure and the width (lamellar layer spacing) of the acicular structure can be controlled by heat treatment. As the microstructure morphology (structure factor) such as the volume fraction of the α phase in the microstructure and the width of the acicular structure changes, the mechanical properties of the alloy changes.

The mechanical properties include various properties such as strength (room-temperature strength, high-temperature strength (creep strength)), impact strength, toughness, and fatigue property. Although each property can be improved by controlling the microstructure, there are some combinations of properties which are incompatible or conflicting with each other in improving multiple strength properties.

FIG. 1 is a table showing the influence of microstructure morphology on mechanical properties of α+β titanium alloys. In FIG. 1, the circle indicates that the microstructure morphology contributes to the mechanical property. Further, in FIG. 1, the cross indicates that the microstructure morphology does not much contribute to the mechanical property.

As shown in FIG. 1, in α'0β titanium alloys, the α phase structure of equiaxed grains, represented by equiaxed a structure in FIG. 1, exhibits, for instance, good fatigue property (high-cycle fatigue strength, fatigue crack occurrence resistance) compared with the acicular structure, but does not much contribute to toughness (fracture toughness) and creep strength, for instance. Further, for instance, in α+β titanium alloys, the acicular structure exhibits, for instance, good toughness (fracture toughness) and creep strength compared with the equiaxed a structure, but does not much contribute to fatigue property (high-cycle fatigue strength, fatigue crack occurrence resistance), for instance. That is, fatigue property tends to conflict with toughness and creep strength in relation to the microstructure morphology.

Therefore, for instance, some α+β titanium alloys have a bi-modal structure combinedly having the α phase structure of equiaxed grains and the acicular structure to balance incompatible or conflicting mechanical properties, as described above. FIG. 2 is a view showing microstructure examples of the α phase of equiaxed grains (equiaxed α phase structure), the acicular structure, and the hi-modal structure including the equiaxed α phase structure and the acicular structure.

The mechanical properties of titanium alloys also vary with the type and the amount of additive element, as described above. Accordingly, it is necessary for titanium alloys to consider not only a parameter relating to the microstructure morphology but also a parameter relating to the composition of the titanium alloys to balance conflicting or incompatible mechanical properties. Therefore, it is not easy to determine the aforementioned various parameters to obtain a desired mechanical property in a titanium alloy.

In this regard, it has been found that it is possible to determine the microstructure morphology of a titanium alloy, based on a relational expression including a mechanical property parameter relating to a mechanical property of the titanium alloy, a microstructure parameter relating to the microstructure morphology of the titanium alloy, and a composition parameter relating to the composition of the titanium alloy.

That is, the method for determining a microstructure of a titanium alloy according to some embodiments determines the microstructure morphology of the titanium alloy, based on any of some later-described relational expressions including a mechanical property parameter relating to a mechanical property of the titanium alloy, a microstructure parameter relating to the microstructure of the titanium alloy, and a composition parameter relating to the composition of the titanium alloy.

With this method, by substituting a desired mechanical property for the mechanical property parameter in the later-described relational expression and substituting the composition of the titanium alloy for the composition parameter in the relational expression, it is possible to obtain a condition which the microstructure parameter has to meet in order to achieve the desired mechanical property. Accordingly, for instance, by performing heat treatment of the titanium alloy so as to obtain microstructure morphology that meets the above condition, it is possible to obtain a titanium alloy having the desired mechanical property. Thus, it is possible to easily determine the microstructure morphology of the titanium alloy to obtain a titanium alloy well balanced with respect to incompatible or conflicting mechanical properties.

Further, in some embodiments, the mechanical property parameter may include a parameter relating to fatigue property and a parameter relating to at least one of toughness or creep strength.

In some embodiments, the microstructure parameter may include a parameter relating to equiaxed α phase area ratio and a parameter relating to lamellar layer spacing.

In some embodiments, the composition parameter may include at least a parameter relating to aluminum content.

As described above, for instance, in an α+β titanium alloy, the α phase structure of equiaxed grains contributes to the improvement of e.g., fatigue property, but does not much contribute to the improvement of e.g., toughness and creep strength. Further, as described above, for instance, in an α+β titanium alloy, the acicular structure contributes to the improvement of e.g., toughness and creep strength, but does not much contribute to the improvement of e.g., fatigue property. That is, fatigue property tends to conflict with toughness and creep strength in relation to the microstructure morphology.

Further, for instance, in an α+β titanium alloy, the influence of aluminum on toughness of the alloy is larger than the influence of other additive elements.

In view of this, in some embodiments, by substituting respective values of a parameter relating to fatigue property, a parameter of at least one of toughness or creep strength, and a parameter relating to aluminum content into the later-described relational expression, it is possible to obtain a condition which the parameter relating to equiaxed a phase area ratio and the parameter relating to lamellar layer spacing have to meet. Further, when a value of one of the parameter relating to equiaxed α phase area ratio or the parameter relating to lamellar layer spacing is determined, a value of the other is also determined.

Accordingly, in some embodiments, by performing heat treatment of the titanium alloy so as to obtain microstructure morphology for achieving the values of the parameter relating to equiaxed α phase area ratio and the parameter relating to lamellar layer spacing as determined above, it is possible to achieve a desired state of mechanical properties which tend to conflict in relation to the microstructure morphology.

That is, the mechanical property parameter includes a parameter relating to strength of the titanium alloy such as creep strength, a parameter relating to toughness of the titanium alloy such as fracture toughness, and a parameter relating to fatigue of the titanium alloy such as high-cycle fatigue limit, for instance. In the method for determining a microstructure of a titanium alloy according to some embodiments, from among parameters included in the mechanical property parameter, at least two parameters which are incompatible or conflicting with each other in relation to the microstructure morphology of the titanium alloy are selected as the parameter substituted into the later-described expression.

Thus, it is possible to easily determine the microstructure morphology of the titanium alloy to obtain a titanium alloy well balanced with respect to at least two incompatible or conflicting mechanical properties.

In some embodiments, the composition parameter may further include at least one parameter of a parameter relating to nitrogen content, a parameter relating to iron content, or a parameter relating to hydrogen content.

Thereby, it is possible to determine the microstructure morphology of the titanium alloy in consideration of the influence of content of at least one of nitrogen, iron, or hydrogen.

In some embodiments, the composition parameter may further include at least one parameter of a parameter relating to carbon content or a parameter relating to vanadium content.

Thereby, it is possible to determine the microstructure morphology of the titanium alloy in consideration of the influence of content of at least one of carbon or vanadium.

(Regarding Relational Expression)

Next, the relational expression according to some embodiments will be described in detail.

The parameter relating to creep strength is creep strength YS [MPa], the parameter relating to toughness is fracture toughness value KIC [MPa√m], and the parameter relating to fatigue property is fatigue limit value σw [MPa].

Further, the parameter relating to equiaxed α phase area ratio is equiaxed α phase area ratio Vα [%], and the parameter relating to lamellar layer spacing is average lamellar layer spacing DL [μm].

Equiaxed α phase area ratio Vα [%] is the proportion of the area of the α phase structure of equiaxed grains in a cross-section of the titanium alloy, and can be determined by quantitatively evaluating the microstructure in the cross-section by image analysis or the like.

Average lamellar layer spacing DL [μm] is an average value of spacing between acicular structures observed in a cross-section of the titanium alloy, and can be determined by quantitatively evaluating the microstructure of the cross-section by image analysis or the like.

Further, the parameter relating to aluminum content is Al [mass %], the parameter relating to nitrogen content is N [mass %], the parameter relating to iron content is Fe [mass %], and the parameter relating to hydrogen content is H [mass %].

A first constant is represented by Const 1, and a1, a2, b1, b2 b3, c1, c2, c3, and c4 each represent a coefficient.

As a result of intensive studies of the present inventors, they have found that the relational expression according to an embodiment can be represented by the following expression (1):

a1 DL−a2×Vα=b1×YS+b2×σw+b3×KIC+c1×Al−c2×N−c3×Fe+c4×H−Const1   (1)

In the expression (1) according to an embodiment, for instance, when the titanium alloy is an α+β titanium alloy such as Ti-6Al-4V alloy, the value of each coefficient a1, a2, b2, b3, c1 , c2, c3, and c4 is as follows.

For instance, coefficient a1 is 30 or more and 300 or less, and coefficient a2 is 1 or more and 10 or less. Further, for instance, coefficient b1 is 0.5 or more and 5 or less, coefficient b2 is 0.1 or more and 2 or less, and coefficient b3 is 5 or more and 50 or less.

Further, for instance, coefficient c1 is 100 or more and 150 or less, coefficient c2 is 1000 or more and 20000 or less, coefficient c3 is 400 or more and 5000 or less, and coefficient c4 is 500 or more and 5000 or less.

In the expression (1), first constant Const1 is 1000 or more and 20000 or less.

Thus, on the basis of the expression (1), it is possible to easily determine the microstructure morphology of the titanium alloy to obtain a titanium alloy well balanced with respect to incompatible or conflicting mechanical properties.

More specifically, for instance, creep strength Ys [MPa], fracture toughness value KIC [MPa√m], and fatigue limit value σw [MPa] required in the titanium alloy are substituted into the expression (1). Further, the composition of the titanium alloy is substituted into the expression (1). Thereby, the value of the right side of the expression (1) is obtained.

Accordingly, when one of equiaxed α phase area ratio Vα [%] or average lamellar layer spacing DL [μm] on the left side of the expression (1) is determined, the other is determined from the expression (1). The same applies to expression (2) according to another embodiment described later.

The relational expression according to another embodiment will now be described.

The parameter relating to carbon content is C [mass %], and the parameter relating to vanadium content is V [mass %].

A second constant is represented by Const 2, and c5 and c6 each represent a coefficient.

The other parameters are same as in the expression (1).

As a result of intensive studies of the present inventors, they have found that the relational expression according to another embodiment can be represented by the following expression (2):

a1×DL−a2×Vα=b1×YS+b2×σw+b3×KIC+c1×Al−c2×N−c3×Fe+c4×H−c5×C+c6×V−Const2   (2)

In the expression (2) according to another embodiment, for instance, when the titanium alloy is an alp titanium alloy such as Ti-6Al-4V alloy, the value of each coefficient a1, a2, b1, b2, b3, c1, c2, c3, c4, c5, and c6 is as follows.

For instance, coefficient a1 is 30 or more and 300 or less, and coefficient a2 is 1 or more and 10 or less.

Further, for instance, coefficient b1 is 0.5 or more and 5 or less, coefficient b2 is 0.1 or more and 2 or less, and coefficient b3 is 5 or more and 50 or less.

Further, for instance, coefficient c1 is 100 or more and 150 or less, coefficient c2 is 1000 or more and 20000 or less, coefficient c3 is 400 or more and 5000 or less, coefficient c4 is 500 or more and 5000 or less, coefficient c5 is 500 or more and 5000 or less, and coefficient c6 is 10 or more and 200 or less.

In the expression (2), second constant Const2 is 1000 or more and 20000 or less.

Thus, on the basis of the expression (2), it is possible to easily determine the microstructure morphology of the titanium alloy to obtain a titanium alloy well balanced with respect to incompatible or conflicting mechanical properties.

(Regarding Process of Deriving Relational Expression)

The above-described relational expressions can be obtained as follows.

As a result of examining a relationship between fracture toughness value KIC and equiaxed α phase area ratio Vα, a relationship between fracture toughness value KIC and equiaxed α phase grain size Dα, and a relationship between fracture toughness value KIC and average lamellar layer spacing DL, there appears to be a correlation between fracture toughness value KIC and these parameters relating to the microstructure morphology, and further, it is found that the fracture toughness value KIC may also be affected by the composition, ductility, and toughness of the titanium alloy.

Then, with respect to fracture toughness value KIC, when the following expression (3) is determined using creep strength YS, average lamellar layer spacing DL, equiaxed α phase grain diameter Dα, and equiaxed α phase area ratio Vα as parameters, a good correlation is found.

KIC=f(YS, DL, Dα, Vα)   (3)

Further, with respect to fatigue property, when the following expression (4) is determined, there is a good correlation between fatigue limit value σw and equiaxed α phase grain size Dα.

σw=f(Dα)   (4)

Since the expressions (3) and (4) both include equiaxed α phase grain size Dα as the parameter, the expression (4) is substituted into the expression (3) to replace the parameter of equiaxed α phase grain size Dα in the expression (3) with the parameter of fatigue limit value σw, and the expressions (1) and (2) are obtained.

(Method for Producing Titanium Alloy)

Hereinafter, a method for producing a titanium alloy according to some embodiments will be described. FIG. 3 is a flowchart for describing a process of the method for producing a titanium alloy according to some embodiments. The method for producing a titanium alloy according to some embodiments is to produce a product made of a titanium alloy such as engine parts and turbine blades from a material of the titanium alloy, and includes a microstructure morphology evaluation step S10, a microstructure parameter determination step S20, a heat treatment condition setting step S30, a property evaluation step S40, and a heat treatment step S50.

(Microstructure Morphology Evaluation Step S10)

The microstructure morphology evaluation step S10 according to some embodiments is a step of calculating a condition which the microstructure parameter has to meet, based on the above-described relational expression. In the microstructure morphology evaluation step S10 according to some embodiments, a value of the mechanical property parameter relating to a mechanical property (target property) required in a product made of a titanium alloy, and a value of the composition of a material of the titanium alloy into the relational expression to calculate a condition which the microstructure parameter has to meet. For instance, in a case where the expression (1) or (2) is used, creep strength YS, fracture toughness value KIC, and fatigue limit value σw are substituted into the expression (1) or (2). Further, the composition of the material of the titanium alloy is substituted into the expression (1) or (2). Thereby, the values on the right side of the expression (1) or (2), i.e., a condition which equiaxed α phase area ratio Vα and average lamellar layer spacing DL on the left side have to meet are determined.

(Microstructure Parameter Determination Step S20)

The microstructure parameter determination step S20 according to some embodiments is a step of determining a value of the microstructure parameter, based on the condition obtained in the microstructure morphology evaluation step S10. FIG. 4 is a flowchart for describing a process of determining a value of the microstructure parameter in the microstructure parameter determination step S20 according to some embodiments. The microstructure parameter determination step S20 according to some embodiments includes a first determination step S21 and a second determination step S22.

The first determination step S21 according to some embodiments is a step of determining a value of one of the parameter relating to equiaxed α phase area ratio or the parameter relating to lamellar layer spacing.

The second determination step S22 according to some embodiments is a step of determining a value of the other of the parameter relating to equiaxed α phase area ratio or the parameter relating to lamellar layer spacing, based on the value of the one parameter determined in the first determination step and the condition obtained in the microstructure morphology evaluation step S10.

In the microstructure parameter determination step S20 according to some embodiments, when a value of one of the parameter relating to equiaxed α phase area ratio or the parameter relating to lamellar layer spacing is determined, a value of the other parameter is also determined based on the condition obtained in the microstructure morphology evaluation step S10.

In the microstructure parameter determination step S20 according to an embodiment, the parameter relating to equiaxed α phase area ratio (equiaxed α phase area ratio Vα) is determined in the first determination step S21, and the parameter relating to lamellar layer spacing (average lamellar layer spacing DL) is determined in the second determination step S22.

For instance, in an α+β titanium alloy, equiaxed α phase area ratio Vα in the microstructure is mainly affected by solution temperature Tst at heat treatment. Further, for instance, in an α+β titanium alloy, average lamellar layer spacing DL in the microstructure is mainly affected by cooling rate dT/dt at solution treatment in heat treatment.

That is, equiaxed α phase area ratio Vα can be controlled by solution temperature Tst, and average lamellar layer spacing DL can be controlled by cooling rate dT/dt at solution treatment.

FIG. 5 is a diagram showing an example of temperature change in heat treatment of a titanium alloy. In some embodiments, heat treatment of the titanium alloy includes solution treatment and annealing. Solution temperature Tst is holding temperature during solution treatment. Cooling rate dT/dt is cooling rate at which a titanium alloy to be subjected to heat treatment is cooled over a period from t1 to t2 in FIG. 5 before annealing, after the titanium alloy is kept at solution temperature Tst for a predetermined period.

Accordingly, in the microstructure parameter determination step S20 according to an embodiment, prior to the second determination step S22, equiaxed α phase area ratio Vα can be determined in the first determination step S21. Thus, it is possible to preferentially determine a condition of solution temperature Tst.

For instance, in a case where solution temperature Tst should be determined first, for instance, due to limitation of heating temperature in a heat treatment facility, equiaxed α phase area ratio Vα may be determined in the first determination step S21, and then average lamellar layer spacing DL may be determined in the second determination step S22.

Further, in the microstructure parameter determination step S20 according to another embodiment, the parameter relating to lamellar layer spacing (average lamellar layer spacing DL) is determined in the first determination step, and the parameter relating to equiaxed α phase area ratio (equiaxed α phase area ratio Vα) is determined in the second determination step.

In the microstructure parameter determination step S20 according to another embodiment, prior to the second determination step S22, average lamellar layer spacing DL can be determined in the first determination step S21. Thus, it is possible to preferentially determine a condition of cooling rate dT/dt for heat treatment.

For instance, if cooling rate dT/dt is set large, difference may occur in actual cooling rate dT/dt between a thick portion and a thin portion of the titanium alloy to be subjected to heat treatment. Accordingly, if cooling rate dT/dt is set large, average lamellar layer spacing DI, may vary between a thick portion and a thin portion of the titanium alloy to be subjected to heat treatment. Thus, it is desired to set cooling rate dT/dt small to reduce variation in average lamellar layer spacing DL with thickness. In this case, average lamellar layer spacing DL may be determined in the first determination step S21, and then equiaxed α phase area ratio Vα may be determined in the second determination step S22.

(Heat Treatment Condition Setting Step S30)

The heat treatment condition setting step S30 according to some embodiments is a step of setting a heat treatment condition for achieving the value of the microstructure parameter determined in the microstructure parameter determination step S20. In the heat treatment condition setting step S30 according to some embodiments, solution temperature Tst at heat treatment for achieving equiaxed α phase area ratio Vα determined in the microstructure parameter determination step S20 is determined. Further, in the heat treatment condition setting step S30 according to some embodiments, cooling rate dT/dt for solution treatment in heat treatment for achieving average lamellar layer spacing DL determined in the microstructure parameter determination step S20 is determined.

In a case where it is difficult to achieve the determined solution temperature Tst and cooling rate dT/dt due to limitation of a facility or the like, the method may return to the microstructure parameter determination step S20, and equiaxed α phase area ratio Vα and average lamellar layer spacing DL may be determined again.

(Property Evaluation Step S40)

The property evaluation step S40 according to some embodiments is a step of performing heat treatment on a specimen under the heat treatment condition set in the heat treatment condition setting step S30 and evaluating whether a target property is satisfied. Here, the target property means a mechanical property required in the titanium alloy (product made of a titanium alloy) according to some embodiments. More specifically, the target property means the value of the mechanical property parameter substituted into the relational expression in the microstructure morphology evaluation step S10. That is, the property evaluation step S40 according to some embodiments is a step of checking whether the composition of a material of the titanium alloy and the heat treatment condition set in the heat treatment condition setting step S30 are appropriate by using the specimen.

FIG. 6 is a flowchart for describing a process of treatment in the property evaluation step S40 according to some embodiments. The property evaluation step S40 according to some embodiments includes a specimen preparation step S41, a specimen evaluation step S42, and a parameter re-setting step 844.

The specimen preparation step 841 according to some embodiments is a step of preparing a specimen by performing heat treatment under the heat treatment condition set in the heat treatment condition setting step S30. That is, in the specimen preparation step S41 according to some embodiments, a specimen is prepared. More specifically, in the specimen preparation step S41 according to some embodiments, a specimen for property evaluation is obtained by forming a specimen from a material of the titanium alloy and performing heat treatment.

The material of the specimen is the material of the titanium alloy having the same composition as that inserted into the relational expression in the microstructure morphology evaluation step S10.

The heat treatment condition for the specimen in the specimen preparation step S41 according to some embodiments is the same as the heat treatment condition set in the heat treatment condition setting step S30.

The specimen evaluation step S42 according to some embodiments is a step of evaluating the mechanical property of the specimen. That is, in the specimen evaluation step S42 according to some embodiments, the mechanical property of the specimen obtained in the specimen preparation step S41 is evaluated. In the specimen evaluation step S42 according to some embodiments, evaluation test relating to the mechanical property parameter inserted into the relational expression in the microstructure morphology evaluation step S10 is performed.

The step S43 is a step of determining whether the value of the microstructure parameter determined in the microstructure parameter determination step S20 is appropriate, based on the evaluation result in the specimen evaluation step S42. That is, in the step S43, it is determined whether the result of evaluation test performed in the specimen evaluation step S42 satisfies the target property.

If the determination is positive in the step S43, i.e., if the result of evaluation test performed in the specimen evaluation step S42 satisfies the target property, the heat treatment step S50 is performed.

If the determination is negative in the step S43, i.e., if the result of evaluation test performed in the specimen evaluation step S42 does not satisfy the target property, the parameter re-setting step S44 is performed.

The parameter re-setting step S44 according to some embodiments is a step of re-setting the heat treatment condition set in the heat treatment condition setting step S30 and the composition of the titanium alloy. That is, in the parameter re-setting step S44 according to some embodiments, for instance, the values of equiaxed α phase area ratio Vα and average lamellar layer spacing DL determined in the microstructure parameter determination step S20 may be modified appropriately so as to achieve the target property. In this case, the method returns to the microstructure parameter determination step S20, and the values of equiaxed a phase area ratio Vα and average lamellar layer spacing DL are modified appropriately.

Further, in the parameter resetting step S44 according to some embodiments, for instance, the composition of the material of the titanium alloy may be modified appropriately so as to achieve the target property. More specifically, if one, e.g., a manufacturer who manufactures the material of the titanium alloy, can control content of each element, he/she may change the composition of the material of the titanium alloy so as to achieve the target property. Further, if one can purchase the material of the titanium alloy, he/she may consider to use another material of the titanium alloy manufactured by another manufacturer. That is, since the material of the titanium alloy may vary in element content depending on manufacturers even within the range of standard, a titanium alloy made by a different manufacturer from that of the titanium alloy initially used may be used to achieve the target property.

In this case, returning to the microstructure morphology evaluation step S10, the composition of the material of the titanium alloy is anew substituted into the expression (1) or (2).

As described above, in the parameter resetting step S44 according to some embodiments, in a ease where it is determined that the value of the microstructure parameter determined in the microstructure parameter determination step S20 is not appropriate in the step S43, at least one of the value of the microstructure parameter or the value of the composition parameter is modified.

Thereby, it is possible to obtain a titanium alloy having the desired mechanical property.

(Heat Treatment Step S50)

The heat treatment step S50 according to some embodiments is a step of performing heat treatment under the heat treatment condition set in the heat treatment condition setting step S30. That is, in the heat treatment step S50 according to some embodiments, a product formed of the material of the titanium alloy which is determined to satisfy the target property in the property evaluation step S40 is subjected to heat treatment under the heat treatment condition which is determined to satisfy the target property in the property evaluation step S40.

With the above-described method for producing a titanium alloy according to some embodiments, by substituting a desired mechanical property for the mechanical property parameter in the relational expression and substituting the composition of the titanium alloy for the composition parameter in the relational expression, it is possible to obtain a condition which the microstructure parameter has to meet in order to achieve the desired mechanical property, and it is possible to determine a value of the microstructure parameter based on the condition.

Further, with the above-described method for producing a titanium alloy according to some embodiments, it is possible to set the heat treatment condition of the titanium alloy so as to obtain microstructure morphology corresponding to the determined microstructure parameter.

Further, with the above-described method for producing a titanium alloy according to some embodiments, by performing heat treatment on the titanium alloy under the set heat treatment condition, it is possible to obtain a titanium alloy having the desired mechanical property. Thus, it is possible to obtain a titanium alloy well balanced with respect to incompatible or conflicting mechanical properties.

The present invention is not limited to the embodiments described above, but includes modifications to the embodiments described above, and embodiments composed of combinations of those embodiments.

For instance, some embodiments were described in conjunction with an α+β titanium alloy. The α+β titanium alloy according to some embodiments is not limited to Ti-6Al-4V alloy, but may be Ti-3Al-2.5V alloy or Ti-6Al-4V-2Sn alloy. 

1. A method for determining a microstructure of a titanium alloy, comprising determining a microstructure morphology of a titanium alloy based on a relational expression including a mechanical property parameter relating to a mechanical property of the titanium alloy, a microstructure parameter relating to a microstructure of the titanium alloy, and a composition parameter relating to a composition of the titanium alloy.
 2. The method for determining a microstructure of a titanium alloy according to claim 1, wherein the mechanical property parameter includes a parameter relating to a fatigue property, and a parameter relating to at least one of toughness or creep strength, wherein the microstructure parameter includes a parameter relating to equiaxed α phase area ratio, and a parameter relating to lamellar layer spacing, and wherein the composition parameter includes at least a parameter relating to aluminum content.
 3. The method for determining a microstructure of a titanium alloy according to claim 2, wherein the composition parameter further includes at least one of a parameter relating to nitrogen content, a parameter relating to iron content, or a parameter relating to hydrogen content.
 4. The method for determining a microstructure of a titanium alloy according to claim 3, wherein when the parameter relating to creep strength is YS [MPa], the parameter relating to toughness is KIC [MPa√m], the parameter relating to the fatigue property is σw [MPa], the parameter relating to equiaxed α phase area ratio is Vα [%], the parameter relating to lamellar layer spacing is DL [μm], the parameter relating to aluminum content is Al [mass %], the parameter relating to nitrogen content is N [mass %], the parameter relating to iron content is Fe [mass %], the parameter relating to hydrogen content is H [mass %]. a first constant is Const1, and a1, a2, b1, b2, b3, c1, c2, c3, and c4 each represent a coefficient, the relational expression is represented by the following expression (1): a1×DL−a2×Vα=b1×YS+b2×σw+b3×KIC+c1×Al−c2×N−c3×Fe+c4×H−Const1   (1), and wherein the coefficient a1 is 30 or more and 300 or less, the coefficient a2 is 1 or more and 10 or less, the coefficient b1 is 0.5 or more and 5 or less, the coefficient b2 is 0.1 or more and 2 or less, the coefficient b3 is 5 or more and 50 or less, the coefficient c1 is 100 or more and 150 or less, the coefficient c2 is 1000 or more and 20000 or less, the coefficient c3 is 400 or more and 5000 or less, the coefficient c4 is 500 or more and 5000 or less, and the first constant Const1 is 1000 or more and 20000 or less.
 5. The method for determining a microstructure of a titanium alloy according to claim 3, wherein the composition parameter further includes at least one of a parameter relating to carbon content or a parameter relating to vanadium content.
 6. The method for determining a microstructure of a titanium alloy according to claim 5, wherein when the parameter relating to creep strength is YS [MPa], the parameter relating to toughness is KIC [MPa√m], the parameter relating to the fatigue property is σw [MPa], the parameter relating to equiaxed α phase area ratio is Vα [%], the parameter relating to lamellar layer spacing is DL [μm], the parameter relating to aluminum content is Al [mass %], the parameter relating to nitrogen content is N [mass %], the parameter relating to iron content is Fe [mass %], the parameter relating to hydrogen content is H [mass %], the parameter relating to carbon content is C [mass %], the parameter relating to vanadium content is V [mass %], a second constant is Const2, and a1, a2, b1, b2, b3, c1, c2, c3, c4, c5, and c6 each represent a coefficient, the relational expression is represented by the following expression (2): a1×DL−a2×Vα=b1×YS+b2×σw+b3×KIC+c1×Al−c2×N−c3×Fe'c4×H−c5×C+c6×V−Const2   (2), and wherein the coefficient a1 is 30 or more and 300 or less, the coefficient a2 is 1 or more and 10 or less, the coefficient b1 is 0.5 or more and 5 or less, the coefficient b2 is 0.1 or more and 2 or less, the coefficient b3 is 5 or more and 50 or less, the coefficient c1 is 100 or more and 150 or less, the coefficient c2 is 1000 or more and 20000 or less, the coefficient c3 is 400 or more and 5000 or less, the coefficient c4 is 500 or more and 5000 or less, the coefficient c5 is 500 or more and 5000 or less. the coefficient c6 is 10 or more and 200 or less, and the second constant Const2 is 1000 or more and 20000 or less.
 7. A method for producing a titanium alloy, comprising a step of calculating a condition which the microstructure parameter has to meet, based on the relational expression according to claim 1, a step of determining a value of the microstructure parameter, based on the condition, a step of setting a heat treatment condition for achieving the determined value of the microstructure parameter, and a step of performing heat treatment under the set heat treatment condition.
 8. The method for producing a titanium alloy according to claim 7, wherein the microstructure parameter includes a parameter relating to equiaxed α phase area ratio, and a parameter relating to lamellar layer spacing, and wherein the step of determining the value of the microstructure parameter includes: a first determination step of determining a value of one parameter of the parameter relating to equiaxed α phase area ratio or the parameter relating to lamellar layer spacing, and a second determination step of determining a value of the other parameter of the parameter relating to equiaxed α phase area ratio or the parameter relating to lamellar layer spacing, based on the value of the one parameter determined in the first determination step and the condition.
 9. The method for producing a titanium alloy according to claim 8, wherein the first determination step includes determining the parameter relating to equiaxed α phase area ratio, and wherein the second determination step includes determining the parameter relating to lamellar layer spacing.
 10. The method for producing a titanium alloy according to claim 8, wherein the first determination step includes determining the parameter relating to lamellar layer spacing, and wherein the second determination step includes determining the parameter relating to equiaxed α phase area ratio.
 11. The method for producing a titanium alloy according to claim 7, further comprising: a step of preparing a specimen by performing heat treatment under the set heat treatment condition; a step of evaluating a mechanical property of the specimen; a step of determining whether the microstructure parameter determined in the step of determining the value of the microstructure parameter is appropriate, based on an evaluation result in the step of evaluating the mechanical property of the specimen; and a step of modifying at least one of the value of the microstructure parameter or a value of the composition parameter if it is determined that the value of the microstructure parameter is not appropriate in the step of determining whether the microstructure parameter is appropriate.
 12. The method for producing a titanium alloy according to claim 8, further comprising: a step of preparing a specimen by performing heat treatment under the set heat treatment condition; a step of evaluating a mechanical property of the specimen; a step of determining whether the microstructure parameter determined in the step of determining the value of the microstructure parameter is appropriate, based on an evaluation result in the step of evaluating the mechanical property of the specimen; and a step of modifying at least one of the value of the microstructure parameter or a value of the composition parameter if it is determined that the value of the microstructure parameter is not appropriate in the step of determining whether the microstructure parameter is appropriate.
 13. The method for producing a titanium alloy according to claim 9, further comprising: a step of preparing a specimen by performing heat treatment under the set heat treatment condition; a step of evaluating a mechanical property of the specimen; a step of determining whether the microstructure parameter determined in the step of determining the value of the microstructure parameter is appropriate, based on an evaluation result in the step of evaluating the mechanical property of the specimen; and a step of modifying at least one of the value of the microstructure parameter or a value of the composition parameter if it is determined that the value of the microstructure parameter is not appropriate in the step of determining whether the microstructure parameter is appropriate.
 14. The method for producing a titanium alloy according to claim 10, further comprising: a step of preparing a specimen by performing heat treatment under the set heat treatment condition; a step of evaluating a mechanical property of the specimen; a step of determining whether the microstructure parameter determined in the step of determining the value of the microstructure parameter is appropriate, based on an evaluation result in the step of evaluating the mechanical property of the specimen; and a step of modifying at least one of the value of the microstructure parameter or a value of the composition parameter if it is determined that the value of the microstructure parameter is not appropriate in the step of determining whether the microstructure parameter is appropriate. 